5-1 Perpendicular Bisectors and Angle Bisectors

5-1 is about perpendiculars and bisectors. There are two goals in this section. The first one is to use properties of perpendicular bisectors. The second one is to use properties of angle bisectors to identify equal distances. A perpendicular bisector is a segment, ray, angle, or line that intersects another segment, ray, angle, or line. The two angles formed by the bisector would be congruent. Also the two sides formed by the bisector would be congruent. Practice problems can be found on pages 268-271 in the text book.

Here are two websites that can help you learn this topic:

http://mathworld.wolfram.com/PerpendicularBisector.html

http://www.mathopenref.com/bisectorperpendicular.html

Here are a few practice problems:

1. What is the measure of angle B if the measure of angle A is 3?

B=3 because A is congruent B.




2. What is the measure of angle CAB if angle BAD = 40 degrees?

Angle CAB = 40 degrees because CAB is congruent to angle BAD and BAD equals 40 degrees.






3. What is the measure of angle AMC?

The measure of angle AMC = ninety degrees because it is congruent to angle CMB and CMB = ninety degrees.




1. Perpendicular Bisector Theorem - Any point that is on the bisector is the same distance from the endpoints of the segment.



2. Converse of the Perpendicular Bisector Theorem - Any point that is the same distance from each endpoint is on the bisector.




3. Angle Bisector Theorem - I a point is on the bisector of an angle, then it is the same distance from the two sides of the angle.





4. Converse of the Angle Bisector Theorem - Any point that is the same distance from the two side angles is on the bisector.






Review Problems:

1. Is point P on the bisector?





2. What is the measure of VT?









3. Is M on the perpendicular bisector?




4. Is P on the perpendicular bisector?